Are you on Windows 7? Check your router is compatible, see this link:

http://www.microsoft.com/windows/usi...d/default.mspx

Delete you username and password if they are stored in the launcher and manually write them in again.

Go to the login page at STO website and try logging in there, http://www.startrekonline.com/

On the launcher for STO select options (top right), choose the EU or US server, probably you are on the US, try the EU proxy

Check Windows, Control Panel, Internet options, Connection Tab, LAN settings at bottom of window and uncheck Proxy Server box if checked

has the STO website been blocked by a program such as spybot?

Check by going to C:\windows\system32\drivers\etc\ and open the hosts file, you can open it with notepad. Do a search for the STO website, if it is listed then save the host file as a backup and then remove this reference to STO and save the hosts file again

Hopefully one of those should get you online